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Existence and bifurcation of integral manifolds with applications

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Abstract

In this paper a bifurcation theorem on the existence of integral manifolds is obtained by using contracting principle. As an application, sufficient conditions for a higher dimensional system to have an integral manifold are given. Especially the existence and uniqueness of a 3-dimensional invariant torus appearing in a 4-dimensional autonomous system with singularity of codimension two are proved.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, 200234, Shanghai, China

    Han Mao’an

  2. Department of Mathematics, Shanghai Jiao Tong University, 200030, Shanghai, China

    Chen Xianfeng

Authors
  1. Han Mao’an
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  2. Chen Xianfeng
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Correspondence to Han Mao’an.

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Mao’an, H., Xianfeng, C. Existence and bifurcation of integral manifolds with applications. Sci. China Ser. A-Math. 48, 940–957 (2005). https://doi.org/10.1007/BF02879076

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  • DOI: https://doi.org/10.1007/BF02879076

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